Evolution of the ionisation energy with the stepwise growth of chiral clusters of [4]helicene

Polycyclic aromatic hydrocarbons (PAHs) are widely established as ubiquitous in the interstellar medium (ISM), but considering their prevalence in harsh vacuum environments, the role of ionisation in the formation of PAH clusters is poorly understood, particularly if a chirality-dependent aggregation route is considered. Here we report on photoelectron spectroscopy experiments on [4]helicene clusters performed with a vacuum ultraviolet synchrotron beamline. Aggregates (up to the heptamer) of [4]helicene, the smallest PAH with helical chirality, were produced and investigated with a combined experimental and theoretical approach using several state-of-the-art quantum-chemical methodologies. The ionisation onsets are extracted for each cluster size from the mass-selected photoelectron spectra and compared with calculations of vertical ionisation energies. We explore the complex aggregation topologies emerging from the multitude of isomers formed through clustering of P and M, the two enantiomers of [4]helicene. The very satisfactory benchmarking between experimental ionisation onsets vs. predicted ionisation energies allows the identification of theoretically predicted potential aggregation motifs and corresponding energetic ordering of chiral clusters. Our structural models suggest that a homochiral aggregation route is energetically favoured over heterochiral arrangements with increasing cluster size, hinting at potential symmetry breaking in PAH cluster formation at the scale of small grains.


Supplementary Computational Details
Photoelectron spectra of the [4]helicene Calculations of the vibrationally-resolved photoelectron spectra (PES) of the [4]helicene molecule were done at the PBE0 1 /def2-TZVPP 2 level of theory.The geometries of the [4]helicene and of its cation in the ground and five excited states were optimized, and the Hessians at each equilibrium structure were computed.The resulting spectrum was computed using the ezFCF (formerly ezSpectrum) program. 3In addition to that, the vertical ionization potentials were computed at the geometry of the neutral [4]helicene.

Structure Setup and Geometry Optimization
The structures given in this work were obtained by the following procedure.
1.The initial structures were obtained by: • global optimization using the ABCluster program; [4][5][6] • generation of trial cluster geometries via Coalescence-Kick software. 7,8 The resulting guess structures were optimized at the GFN2-xTB level of theory 9 using the XTB software.10 3. Onlye structures with relative energy smaller than 300 K (210 cm −1 ) were kept for each cluster size/type (i.e., for each n and m in cluster P n M m ). 4. All the structures were adjusted to have the center of mass as the coordinates origin.
5. The distance matrix D (consisting of elements D αβ ) between the kept structures was calculated by minimizing the functional The r αβ ij = |r α i − R(φ, θ, χ)r β j | is the distance between the coordinates of the atom #i of structure α and atom #j of structure β, that was rotated via rotation matrix R dependent on three Euler angles (φ, θ, χ).Weights w αβ ij are calculated via equation: here R i denotes atomic radius of the atom i, which was taken 0.53 Å for the hydrogens, and 1.20 Å for carbons.Scale coefficient s was taken to be 50.Atoms i and j were considered as the same type if: • they had the same nuclei charge, • they had the same number of chemically-bonded neighbours, • the masses of their chemically-bonded neighbours were the same.
Minimzation was performed using differential evolution algorithm as implemented in the SciPy library.
6.The structures α and β were considered to be the same, if the following criterion was fulfilled: where θ is the threshold value taken to be 0.05, and max(D α β ) is the maximal value of the distance matrix D.
7. Amongst the same structural isomers, the lowest energy ones are taken.
Steps 2-6 above are performed via a script findUniqueConformers.py of the Molinc project. 11

Calculation of Vertical Ionization Potentials
0][21][22] In case of DLPNO-CCSD(T), the total energies of the neutral and cationic complexes were calculated, where the energy difference is the vIP.In case of IP-EOM-DLPNO-CCSD the vIPs were directly obtained from the calculation.Both types of calculations were performed using the Orca 23,24 program package.For all calculations the cc-pVTZ 25 basis set and NormalPNO thresholds were used.To reduce computational cost, the resolutionof-the-identity (RI) approximation in conjunction with the auxiliary Coulomb fitting bases cc-pVTZ/C 26 and Def2/J 27,28 was employed.Additionally, the chain-of-spheres exchange (COSX) algorithm 29 was applied to numerically fit the exchange integrals to further reduce the computational cost.For the combination of diabatic ionization potentials obtained with subsystem-based G 0 W 0 and electronic couplings from FDE-ET a locally modified version of the Serenity 30,31 program was used.All calculations were carried out using the cc-pVTZ 25 basis set.To reduce computational cost, the RI approximation in conjunction with the auxiliary Coulomb fitting basis Def2/J 27,28 was employed.For the FDE-ET and G 0 W 0 calculations the PBE 32 and BHLYP 33,34 exchange-correlation (XC) functionals were used, respectively.For the non-additive contributions the PW91 35,36 XC functional was used in combination with the conjoint 37 kinetic-energy functional PW91k. 38Mutual relaxations of subsystem densities were accounted for using Freeze-and-Thaw (FaT) cycles. 39Three such cycles were found sufficient to obtain accurate electronic densities (see also Refs.40-42).The FDE-ET electronic couplings V ij were calculated by coupling two quasi-diabatic states Φ i and Φ j , where helicene monomer i or j is charged, including all subsystems contained in a cluster.
To give an example, to calculate V 12 of the complex dimer the states and ] are constructed and coupled.In case of e.g. the tetramer V 12 is cal- Here, i hel corresponds to one of the helicene monomers.For obtaining diabatic ionization potentials H ii , G 0 W 0 calculations were carried out including the energetically highest occupied and lowest virtual orbitals.Furthermore, 60 integration points, obtained from a modified Gauss-Legendre quadrature, along the imaginary frequency axes have been employed throughout.The analytic continuation approach 43 was employed using 16 Padé points. 44,45r each complex electronic couplings V ij and diabatic diabatic ionization potentials H ii were obtained and assembled in a matrix M whose elements are defined by and M ij = H ii for i = j.This matrix is diagonalized and a set of eigenvalues is obtained.
The lowest eigenvalue provides the lowest vIP for each helicene complex.
In addition to the fully ab initio methods, we have also applied the two semi-empirical methods of calculating the vIPs: • DFTB-CI, 46,47 from the deMonNano package, 48 • IP-xTB2 model from the XTB package. 10

Racemization barrier of [4]helicene monomer and dimer
Supplementary Here, the difference between DFT and DLPNO-CCSD(T) energies is more noticeable, probably because of the decrease in the basis set for DFT, but also probably due to the higher role of the dispersion interaction in the dimer.Thus, the ZPVE-corrected values and Gibbs free energy barrier were only computed at the DLPNO(NormalPNO)-CCSD(T)/cc-pVTZ//PBE0-D3(BJ) level of theory.ZPVE-corrected barriers are 0.28 eV for conversion PM→PP and 0.26 eV for conversion PP→PM.Gibbs free energy barriers at 298 K are 0.31 eV for conversion PM→PP and 0.29 eV (for conversion PP→PM).
The comparison of the relative electronic energies at the DLPNO-CCSD(T)/cc-pVTZ//DFT level of theory for P↔M and PM↔PP interconversions, as well as ES and TS structures are given in Figure 1.All the calculations were performed using ORCA software.

Theoretical ionization potentials of the [4]helicene clusters
In the main text, a lowest-energy structure set A according to the GFN2-xTB electronic energies has been defined.This has been done for reasons of consistency with the geometry optimization of these structures that has been carried out using the same method.In this supplementary material, we will consider an additional lowest-energy structure set B according to electronic energies obtained with DLPNO-CCSD(T) (see Tab. for nearly each [4]helicene cluster.The deviation from the experimental ITs increases for the cluster sizes 6 and 7. Fig. 2 indicates that for those cluster sizes, there are conformers with a vIP perfectly reproducing the experimental IT.However, those conformers do not belong to the earlier mentioned structure set B with the lowest electronic ground-state energy according to DLPNO-CCSD(T) (see Tab. 6 and Fig. 3).For smaller cluster sizes the overall trend of the ITs is very well reproduced.The same holds for the vIPs calculated with IP-EOM-DLPNO-CCSD.In contrast to DLPNO-CCSD(T) or G 0 W 0 -FDE-ET the vIPs are shifted to smaller values and, thus, underestimate the experimental ITs.Fig. 4 shows the kernel-density estimation 50,51 (KDE) curves and root-mean square deviation (RMSD) of the difference of the DLPNO-CCSD(T), IP-EOM-DLPNO-CCSD and G 0 W 0 -FDE-ET vIPs with respect to (w.r.t.) the experimental ionization thresholds calculated using the Seaborn 52,53 Python library.The difference of the theoretical and experimental values where calculated for every [4]helicene cluster and the probability density function (PDF) was calculated using the KDE method.When comparing the KDE curves it can be seen that the curve of G 0 W 0 -FDE-ET is the most narrow, while IP-EOM-DLPNO-CCSD shows a wide distribution of possible vIPs.Additionally, the maximum of the G 0 W 0 -FDE-ET KDE curve is the closest to 0 eV, which indicates that this method provides the most accurate results beneath the three chosen approaches.
[4]helicene + state number vIP aIP 0 7. 4   Supplementary Figure 4: Kernel-density estimation curves of the difference of the calculated vIPs (in units of eV) with respect to the experimental ionization thresholds.Supplementary Table 3: Diabatic ionization energies H ii (in units of eV) calculated for each [4]helicene cluster using the subsystem-based G 0 W 0 approach.(in units of eV) for different [4]  Supplementary Figure 5: Fitting results for the ionization thresholds of [4]helicene clusters ((Hel) n ) as described above.

Figure 1 :
Racemization barriers.Comparison of calculated activation energies for the racemization of the[4]helicene monomer and dimer.The equilibrium structure (ES) and a planar transition state (TS) of the neutral[4]he-licene were optimized at the PBE0-D3(BJ)/def2-TZVPP level of theory.For both the optimized structures at DLPNO(TightPNO)-CCSD(T)/cc-pVTZ, single-point energies were computed.The electronic energy difference between the TS and ES was found to be 0.19 eV (18 kJ mol −1 ) at both PBE0-D3(BJ)/def2-TZVPP and DLPNO(TightPNO)-CCSD(T)/cc-pVTZ//PBE0-D3(BJ)/def2-TZVPP levels of theory.The zero-point-energy-corrected barrier height is 0.18 eV, and the Gibbs free energy barrier at 298 K is 0.19 eV.A similar calculation for the interconversion barrier for PP PM was performed.The lowest energy PP and PM clusters of[4]helicene at GFN2-xTB level of theory were reoptimized at the PBE0-D3(BJ)/def2-SV(P) level of theory.The harmonic frequency calculation confirmed the ES structures at the same level of theory.The basis set was reduced from def2-TZVPP to def2-SV(P) to deal with the increasing cost of the calculation in the case of the TS search.For the two optimized ES of PP and PM, a climbing image nudged elastic band method (CI-NEB) TS search49 and consecutive harmonic frequency calculation were performed at the PBE0-D3(BJ)/def2-SV(P) level of theory.The energies of the two ES and of the TS were recomputed at the DLPNO(NormalPNO)-CCSD(T)/cc-pVTZ//PBE0-D3(BJ)/def2-SV(P) level of theory.The electronic energy differences between the TS and ES were found to be • 0.23 eV (23 kJ mol −1 ) for conversion PM→PP and 0.22 eV (21 kJ mol −1 ) for conversion PP→PM at the PBE0-D3(BJ)/def2-SV(P) level of theory;• 0.28 eV (27 kJ mol −1 ) for conversion PM→PP and 0.27 eV (26 kJ mol −1 ) for conversion PP→PM at the DLPNO(NormalPNO)-CCSD(T)/cc-pVTZ//PBE0-D3(BJ)/def2-SV(P) level of theory.

Table 2 :
Vertical ionization potentials of the lowest energy[4]helicene clusters (vIP) and relative energies of each cluster geometry with respect to the lowest structure of the same size (∆E).The geometries and energies (∆E) were obtained with GFN2-xTB.The vIPs were computed using DLPNO-CCSD(T), IP-EOM-DLPNO-CCSD, G 0 W 0 -FDE-ET, DFTB-CI, and IP-xTB2.The vIPs are given in units of eV, ∆E values are given in units of cm −1 .# indicates the isomer number with respect to the most stable (#=0) for each cluster type.

Table 7 :
helicene cluster conformers.Dissociation energies (D e , in eV) for the evaporation of a monomer from the neutral and cation clusters.The neutral values have been extracted using the energies for the most stable structures in Table6, while the ionisation energies needed to calculate the cationic values have been taken from Table2, using the G 0 W 0 −FDE-ET method which is in good agreement with the experimental results.
n D e (M n → M n−1 + M ) D e (M + n → M + n−1 + M )